In the age of massive data, the construction of knowledge graph has increasingly become a forceful support for the downstream applications of artificial intelligence. However, the information of entities in knowledge graphs is usually incomplete, so it is urgent to supplement the relations of entities through entity alignment task. Frustratingly, the current entity alignment models are facing serious challenges. First, some models only focus on structural features and other auxiliary information (e.g., attributes, images and descriptions), but ignore the features of the entity itself can be scaled resulting in over-smoothing issue. Second, most models utilize higher-order networks to aggregate neighborhood information by stacking layers, but the training cost of these models are drastically higher. Third, most models are supervised or semi-supervised, but there are few pre-aligned seeds for alignment, which greatly limits the improvement of model performance. Hence, to address the above three issues, we propose a Higher-Order Graph Neural Network with Local Inflation for entity alignment, named HOLI-GNN. Specifically, we introduce a local inflation mechanism, which enlarges the each feature of entities to mitigate the impact of over-smoothing caused by neighborhood aggregation. Additionally, we propose a novel higher-order encoder to capture higher-order information. Furthermore, our model also employ currently popular iteration strategy to increase labeled entity pairs, which can markedly promote the performance of align task. Finally, we perform comprehensive experiments to validate the effectiveness of our model on benchmark datasets. The results strongly indicate that our model exhibits better performance than the state-of-the-art models.